Geometry of Linear Matrix Inequalities
A Course in Convexity and Real Algebraic Geometry with a View Towards Optimization
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Beschreibung
This textbook provides a thorough introduction to spectrahedra, which are the solution sets to linear matrix inequalities, emerging in convex and polynomial optimization, analysis, combinatorics, and algebraic geometry. Including a wealth of examples and exercises, this textbook guides the reader in helping to determine the convex sets that can be represented and approximated as spectrahedra and their shadows (projections). Several general results obtained in the last 15 years by a variety of different methods are presented in the book, along with the necessary background from algebra and geometry.
This textbook provides a thorough introduction to spectrahedra, which are the solution sets to linear matrix inequalities, emerging in convex and polynomial optimization, analysis, combinatorics, and algebraic geometry. Including a wealth of examples and exercises, this textbook guides the reader in helping to determine the convex sets that can be represented and approximated as spectrahedra and their shadows (projections). Several general results obtained in the last 15 years by a variety of different methods are presented in the book, along with the necessary background from algebra and geometry.
Unifies recent key results, along with elementary proofs Includes many exercises for active learning Appeals to mathematical researchers across diverse fields
Autor*in
Tim Netzer
Themen in »Geometry of Linear Matrix Inequalities«
Real Algebraic Geometry Convex Geometry Matrices Polynomial Optimization Sums of Squares Eigenvalues Semidefinitie Programming Convex Optimization Extended Formulations Non-commutative Geometry Hyperbolic Polynomials Real Algebraic Curves
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"This book is part of Birkhäuser 'Compact Textbooks in Mathematics' series, which aims for concise books that are tailored in size and scope to a single semester course at a late undergraduate or early graduate student level. This book fits that bill precisely. ... There are two appendices, one on real algebraic geometry and one on convexity, which provide background. With these, the book is in principle self-contained … ." (Tamon Stephen, Mathematical Reviews, March, 2025)
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